1965 Barracuda Trans help

Noob here needs help with his "new to him", first ever, barracuda.

Car: 1965 Cuda, 273 2bbl, 904 torqueflite, consonle shifter. Runs and drives fine in all gears.

Problem: when the shift lever is put in park, it still rolls front and back.

So far:

1)jacked up car, checked cables at trans. I have 2 cables connected to trans, both in poor shape with cracking and missing rubber housing.
Both cables seem too long and are wired away from the header which has probably melted one cable in the past. Trans is leaking somewhere around there too.
2)Removed console and found the shift cable attached, but other cable disconnected. It's just lying under the console. I can kinda guess where it goes and probably needs a cotter pin to stay in the shifter, but it's way too long.

Is this disconnected cable a "park" cable, and if so how does it work?

Thanks in advance for any help. I'm waiting on the shop manual now, I just want to get things started and try to pass inspection and actually drive this car more than around the block.

thanks,
Kevin and the Bondo-cuda.